已知二次函数f(x)=ax的平方+x,若X属于【0 1】时有f(x)的绝对值小于等于1恒成立,则实数af(x)=-x满足,对于任意的 属于【0,1】都有f()-f()的绝对值小于等于1恒成立,则a的取值范围
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已知二次函数f(x)=ax的平方+x,若X属于【0 1】时有f(x)的绝对值小于等于1恒成立,则实数af(x)=-x满足,对于任意的 属于【0,1】都有f()-f()的绝对值小于等于1恒成立,则a的取值范围
已知二次函数f(x)=ax的平方+x,若X属于【0 1】时有f(x)的绝对值小于等于1恒成立,则实数a
f(x)=-x满足,对于任意的 属于【0,1】都有f()-f()的绝对值小于等于1恒成立,则a的取值范围
已知二次函数f(x)=ax的平方+x,若X属于【0 1】时有f(x)的绝对值小于等于1恒成立,则实数af(x)=-x满足,对于任意的 属于【0,1】都有f()-f()的绝对值小于等于1恒成立,则a的取值范围
若X属于【0 1】时有f(x)的绝对值小于等于1恒成立
即当x∈[0,1]时,-1≤f(x)≤1
即在[0,1]内,这个二次函数的最大值小于1,最小值大于-1
f'(x)=2ax+1=0 解得x=-1/2a
当-1/2a<0,即a>0时,
f(0)为最小=0>-1成立;
f(1)为最大=a+1 因为a>0,所以1+a>1,不满足条件 舍掉
当-1/2a>1,即a<-2时,
f(0)为最大=0<1成立;
f(1)为最小=a+1 因为a<-2,所以a+1<-1,不满足条件,舍掉
当0≤-1/2a≤1 即-2≤a≤0时
f(-1/2a)为最大=1/4a-1/2a=-1/4a 这里-1/4a≤1,解得-4a≥1,得a≤-1/4
f(0)=0 满足条件
f(1)=a+1 满足a+1>-1,即a>-2
综上,a的取值范围为[-2,-1/4]
对函数求导,得f'(x)=2ax+1,
令f'(x)=0,即2ax+1=0 解得x=-1/2a
若-1/2a<0,即a>0时,
f(0)=0,属于[-1,1],符合条件;
f(1)=a+1 因为a>0,所以1+a>1,不满足条件,所以-1/2a<0 不成立;
若-1/2a>1,即a<-2时,
f(0)=0属于[-1,1],符合条件;
f(1...
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对函数求导,得f'(x)=2ax+1,
令f'(x)=0,即2ax+1=0 解得x=-1/2a
若-1/2a<0,即a>0时,
f(0)=0,属于[-1,1],符合条件;
f(1)=a+1 因为a>0,所以1+a>1,不满足条件,所以-1/2a<0 不成立;
若-1/2a>1,即a<-2时,
f(0)=0属于[-1,1],符合条件;
f(1)=a+1 因为a<-2,所以a+1<-1,不满足条件,所以-1/2a>1 不成立;
则有 0≤-1/2a≤1 即-2≤a≤0;
当x>-1/2a时,f'(x)>0,函数单调递增,当x<-1/2a时,f'(x)<0,函数单调递减,
f(0)=0, f(1)=a+1,f(-1/2a)=1/4a-1/2a=-1/4a 都属于[-1,1]
得a的范围为[-2,-1/4]
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1) a>0时,开口向上,对称轴x=-1/2a<0,f(x)在【0 1】单调增,f(0)=0,
则f(1)=a+1≤1,即a≤0,矛盾所以不存在。
2)a<0时,开口向下,对称轴x=-1/2a>0,
a)当对称轴x=-1/2a>1时,即-1/2<a<0时,f(x)在【0 1】单调增,f(0)=0,
则f(1)=a+1≤1,即a≤0,所以-1/2<a<0
b)...
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1) a>0时,开口向上,对称轴x=-1/2a<0,f(x)在【0 1】单调增,f(0)=0,
则f(1)=a+1≤1,即a≤0,矛盾所以不存在。
2)a<0时,开口向下,对称轴x=-1/2a>0,
a)当对称轴x=-1/2a>1时,即-1/2<a<0时,f(x)在【0 1】单调增,f(0)=0,
则f(1)=a+1≤1,即a≤0,所以-1/2<a<0
b)当对称轴x=-1/2a∈(0,1】时,即a≤-1/2,
所以有f(0)=0∈[-1,1],f(1)=a+1∈[-1,1],f(-1/2a)=-1/4a∈[-1,1],
即,-2≤a≤0且a≤-1/4,所以-2≤a≤-1/2。
由a)。b)得到-2≤a<0
综上得到-2≤a<0
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Money Master Basketball shoes Ugg Boots For females Be able to get Additional info In regard to Dunkle Ugg Boots? Learn Correct
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Money Master Basketball shoes Ugg Boots For females Be able to get Additional info In regard to Dunkle Ugg Boots? Learn Correct
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